”集合状”かｗ、これ意味わからんと思ったが（＾＾ ”Every set model of ZF is set-like and extensional. ”の「set-like」の直訳だね（＾＾；
＜参考引用、該当英文箇所＞ (なお、Applicationも、”応用”より”適用”が適訳かもね。微妙だが) https://en.wikipedia.org/wiki/Mostowski_collapse_lemma Mostowski collapse lemma (抜粋) Application Every set model of ZF is set-like and extensional. If the model is well-founded, then by the Mostowski collapse lemma it is isomorphic to a transitive model of ZF and such a transitive model is unique.
Saying that the membership relation of some model of ZF is well-founded is stronger than saying that the axiom of regularity is true in the model. There exists a model M (assuming the consistency of ZF) whose domain has a subset A with no R-minimal element, but this set A is not a "set in the model" (A is not in the domain of the model, even though all of its members are). More precisely, for no such set A there exists x in M such that A = R^-1 [x]. So M satisfies the axiom of regularity (it is "internally" well-founded) but it is not well-founded and the collapse lemma does not apply to it. (引用終り) 以上
